The question is whether an illegal immigrant even has access to due process, according to a strict legal reading of the law. This was one of the arguments being thrown around - whether or not "any person" in the above applies to illegal immigrants or just US-born noncitizens (native american indians? I forget).
I think you completely missed the point of my reference to the 14th.
Edit: btw the "within its jurisdiction" phrase above is probably why the supreme court is treading so carefully around the el salvador part of this - they can't give the administration any grounds to point out that el salvador is outside US jurisdiction. That's why all they could say was 'facilitate', and why they had to slap the lower judge's wrist.